Question

The triangle formed by joining the mid-points of an equilateral triangle is triangle.

• A. an equilateral
• B. an isosceles
• C. a scalene

Answer 1

The correct option is A an equilateral

$△$ABC is an equilateral triangle. D, E and F are mid points of sides AB, BC and AC respectively.

By mid point theorem,

$DE\parallel AC$ and $DE=\frac{1}{2}AC$ ... (i)

$DF\parallel BC$ and $DF=\frac{1}{2}BC$ ... (ii)

$EF\parallel AB$ and $EF=\frac{1}{2}AB$ ... (iii)

Since ABC is an equilateral triangle, $AB=BC=AC$

Therefore, $DE=DF=EF=\frac{1}{2}AB$

Hence, $△$ DEF is an equilateral triangle.